Electrostatics of a simple membrane model using Green's functions formalism

Biophysical Journal

Volumn 71, Issue 2, 1996, Pages 795-810

  Von Kitzing, Eberhard ^a   Soumpasis, Dikeos Mario ^b  

^a MAX PLANCK INSTITUTE FOR MEDICAL RESEARCH   (Germany)

^b MAX PLANCK INSTITUTE FOR BIOPHYSICAL CHEMISTRY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BILAYER MEMBRANE; COMPUTER MODEL; ION TRANSPORT; MATHEMATICAL ANALYSIS; MEMBRANE CURRENT;

EID: 0029739061     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0006-3495(96)79281-0     Document Type: Article

References (114)

1. Akabas, M. H., C. Kaufmann, P. Archdeacon, and A. Karlin. 1994. Identification of acetylcholine-receptor channel-lining residues in the entire M2 segment of the α-subunit. Neuron. 13:919-927.
2. Aleman, C., M. Orozco, and F. J. Luque. 1994. Multicentric charges for the accurate representation of electrostatic interactions in force-field calculations for small molecules. Chem. Phys. 189:573-584.
3. Alvarez O., A. Villarroel, and G. Eisenman. 1992. Calculation of ion currents from energy profiles and energy profiles from ion currents in multibarrier, multisite, multioccupancy channel model. Methods Enzymol. 207:816-854.
4. Andersen, O. S., and R. E. Koeppe II. 1992. Molecular determinants of channel function. Physiol. Rev. 72:S89-S158.
5. + by the gramicidin channel. Comm. Mol. Cell Biophys. 6:91-110.
6. + by gramicidin A. Biophys. J. 56:171-182.
7. Bayley, C. I., P. Cieplak, W. D. Cornell, and P. A. Kollman. 1993. A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model. J. Phys. Chem. 97:10269-10280.
8. Bek, S., and E. Jakobsson. 1994. Brownian dynamics study of a multiplyoccupied cation channel: application to understanding permeation in potassium channels. Biophys. J. 66:1028-1038.
9. Bharadwaj, R., A. Windemuth, S. Sridharan, B. Honig, and A. Nicholls. 1995. The fast multipole boundary element method for molecular electrostatics - an optimal approach for large systems. J. Comput. Chem. 16:898-913.
10. Boiko, I. I. 1993. The Electron Gas Kinetic Due to the Interaction of the Gas with the Fluctuating Potential (Russian). Nauka Dumka, Kiev.
11. Bopp, P. A., A. A. Kornyshev, and G. Sutmann. 1996. Static nonlocal dielectric function of liquid water. Phys. Rev. Lett. 76:1280-1283.
12. Born, M. 1920. Volumen und Hydratationswärme der Ionen. Z. Phys. 1:45-48.
13. Cafiso, D. S. 1994. Alamethicin - a peptide model for voltage gating and protein membrane interactions. Annu. Rev. Biophys. Biomol. Struct. 23:141-165.
14. Changeux, J.-P. 1990. The nicotinic acetylcholine receptor: an allosteric protein prototype of ligand-gated ion channels. Trends Pharmacol. Sci. 11:485-491.
15. Charnet, P., C. Labarca, R. J. Leonard, N. Vogelaar, L. Czyzyk, A. Gouin, N. Davidson, and H. Lester. 1990. An open-channel blocker interacts with adjacent turns of α-helices in the nicotinic acetylcholine receptor. Neuron. 2:87-95.
16. Cooper, K., E. Jakobsson, and P. Wolynes. 1985. The theory of ion transport through membrane channels. Prog. Biophys. Mol. Biol. 46: 51-96.
17. Cornell, W. D., P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz, D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell, and P. A. Kollman. 1995. A 2nd generation force-field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117:5179-5197.
18. Cramer, C. J., and D. G. Truhlar. 1992. An SCF solvation model for the hydrophobic effect and absolute free energies of aqueous solvents. Science. 256:213-217.
19. Darden, T., D. York, and L. Pedersen. 1993. Particle mesh Ewald: an (N log N) method for Ewald sums in large systems. J. Chem. Phys. 98: 10089-10092.
20. Dilger, J. P., L. R. Fisher, and P. A. Haydon. 1982. A critical comparison of electrical and optical methods for bilayer thickness determination. Chem. Phys. Lipids. 30:159.
21. Dinur, U., and A. T. Hagler, 1989. Determination of atomic point charges and point dipoles from the Cartesian derivatives of the molecular dipole moment and second moments, and from energy second derivatives of planar dimers. (1) Theory. J. Chem. Phys. 91:2949-2970.
22. Dorman, V., M. B. Partenskii, and P. C. Jordan. 1996. A semimicroscopic Monte Carlo study of permeation energetics in a gramicidin-like channel - the origin of cation selectivity. Biophys. J. 70:121-134.
23. Dosen-Micovic, L., and N. L. Allinger. 1978. The effects of electrostatic interactions and solvation energies on conformational equilibria in dihalides and haloketones. Tetrahedron. 34:3385-3393.
24. Eisenberg, D., M. Wesson, and M. Yamashita. 1989. Interpretation of protein folding and binding with atomic solvation parameters. Chim. Scripta. 29A:217-221.
25. Eisenberg, R. S. 1996a. Atomic biology, electrostatics, and ionic channels. In New Developments and Theoretical Studies of Proteins. R. Elber, editor. World Scientific Publishing, Philadelphia.
26. Eisenberg, R. S. 1996b. Computing the field in proteins and channels. J. Membr. Biol. 150:1-25.
27. Eisenman, G., and O. Alvarez. 1991. Structure and function of channels and channelogs as studied by computational chemistry. J. Membr. Biol. 119:109-132.
28. Eisenman, G., A. Villarroel, M. Montai, and O. Alvarez. 1990. Energy profiles for ion permeation in pentameric protein channels: from viruses to receptor channels. In Progress in Cell Research. J. M. Ritchie. P. J. Magistretti, and L. Bolis, editors. Springer Verlag, New York. 195-211.
29. Eyring, H., R. Lumry, and J. W. Woodbury. 1949. Some applications of modern rate theory to physiological systems. Rec. Chem. Prog. 10: 100-114.
30. Furois-Corbin, S., and A. Pullman. 1991. The effect of point mutations on energy profiles in a model of the nicotinic acetylcholine receptor channel. Biophys. Chem. 39:153-159.
31. Hagler, A. T., and C. S. Ewig. 1994. On the use of quantum energy surfaces in the derivation of molecular force fields. Comp. Phys. Commun. 84:131-155.
32. Halgren, T. A. 1995. Potential energy functions. Curr. Opin. Struct. Biol. 5:205-210.
33. Harvey, S. C. 1989. Treatment of electrostatic effects in macromolecular modeling. Proteins. 5:78-92.
34. Hawkins, G. D., C. J. Cramer, and D. G. Truhlar. 1995. Pairwise solute descreening of solute charges from a dielectric medium. Chem. Phys. Lett. 246:122-129.
35. Hille, B. 1992. Ionic Channels of Exitable Membranes. Sinauer Associates, Sunderland, MA.
36. Holm, L., and C. Sander. 1992. Evaluation of protein models by atomic solvation preference. J. Mol Biol. 225:93-105.
37. Hummer, G., L. R. Pratt, and A. E. Garcia. 1996. Free energy of ionic hydration. J. Phys. Chem. 100:1206-1215.
38. Hyun, J. K., C. S. Babu, and T. Ichiye. 1995. Apparent local dielectric response around ions in water - a method for its determination and its applications. J. Phys. Chem. 99:5187-5195.
39. Imoto, K., C. Busch, B. Sakmann, M. Mishina, T. Konno, J. Nakai, H. Bujo, Y. Mori, K. Fukuda, and S. Numa. 1988. Rings of negatively charged amino acids determine the acetylcholine receptor channel conductance. Nature. 335:645-648.
40. Imoto, K., T. Konno, J. Nakai, F. Wang, M. Mishina, and S. Numa. 1991. A ring of uncharged polar amino acids as a component of channel constriction in the nicotinic acetylcholine receptor. FEBS Lett. 289: 193-200.
41. Imoto, K., C. Methfessel, B. Sakmann, M. Mishina, Y. Mori, T. Konno, K. Fukuda, M. Kurasaki, H. Bujo, Y. Fujita, and S. Numa. 1986. Location of a δ-subunit region determining ion transport through the acetylcholine receptor channel. Nature. 324:670-674.
42. Jackson, J. D. 1962. Classical Electrodynamics. John Wiley, New York.
43. Jakobsson, E. 1993. Hierarchies of simulation methods in understanding biomolecular function. Int. J. Quant. Chem. 1993:25-36.
44. Jakobsson, E., and S.-W. Chiu. 1988. Application of Brownian motion theory to the analysis of membrane channel ionic trajectories calculated by molecular dynamics. Biophys. J. 54:751-756.
45. Jordan, P. C. 1981. Energy barriers for passage of ions through channels. Exact solution of two electrostatic problems. Biophvs. Chem. 13: 203-212.
46. Jordan, P. C. 1982. Electrostatic modeling of ion pores. (1) Energy barriers and electric field profiles. Biophys. J. 39:157-164.
47. Jordan, P. C. 1983. Electrostatic modeling of ion pores. (2) Effects attributable to the membrane dipole potential. Biophys. J. 41:189-195.
48. Jordan, P. C. 1990. Ion-water and ion-polypeptide in a gramicidin-like channel: a molecular dynamics study. Biophys. J. 58:1133-1156.
49. Jordan, P. C. 1993. Interactions of ions with membrane proteins. In Thermodynamics of Membrane Receptors and Channels. M. B. Jackson, editor. CRC Press, Boca Raton, FL. 27-80.
50. Juffer, A. H., and H. J. C. Berendsen. 1993. Surface Boundary Conditions: A Simulation Model for Macromolecules. Springer-Verlag, Berlin, Heidelberg. 137-156.
51. Juffer, A. H., E. F. F. Botta, B. A. M. van Keulen, A. van der Ploeg, and H. J. C. Berendsen. 1991. The electric potential of a macromolecule in a solvent: a fundamental approach. J. Comput. Phys. 97:144-171.
52. Karlin, A. 1991. Explorations of the nicotinic acetylcholine receptor. Harvey Lecture Ser. 85:71-107.
53. Kerr, I. D., R. Sankararamakrishnan, O. S. Smart, and M. S. P. Sansom. 1994. Parallel helix bundles and ion channels - molecular modeling via simulated annealing and restrained molecular dynamics. Biophys. J. 67:1501-1515.
54. Kirkwood, J. G. 1934. Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J. Chem. Phys. 2:351-361.
55. Konno, T., C. Busch, E. von Kitzing, K. Imoto, F. Wang, J. Nakai, M. Mishina, S. Numa, and B. Sakmann. 1991. Rings of anionic amino acids as structural determinants of ion selectivity in the acetylcholine receptor channel. Proc. R. Soc. Lond. B. 244:69-79.
56. Kornyshev, A. A., and G. Sutmann. 1996. The shape of the nonlocal dielectric function of polar liquids and the implications for thermodynamic properties of electrolytes - a comparative study. J. Chem. Phys. 104:1524-1544.
57. Kramers, H. A. 1940. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica. 7:284-304.
58. Kuwajima, S., and A. Warshel. 1988. The extended Ewald method: a general treatment of long-range electrostatic interactions in microscopic simulations. J. Chem. Phys. 89:3751-3759.
59. Lavery, R., K. Zakrzewska, and A. Pullman. 1984. Optimized monopole expansions for the representation of the electrostatic properties of the nucleic acids. J. Comput. Chem. 5:363-373.
60. Lee, F. S., and A. Warshel. 1992. A local reaction field method for fast evaluation of long-range electrostatic interactions in molecular simulations. J. Chem. Phys. 97:3100-3107.
61. Leonard, R. J., C. G. Labarca, P. Chanet, N. Davidson, and H. A. Lester. 1988. Evidence that the M2 membrane-spanning region lines the ion channel pore of the nicotinic receptor. Science. 242:1578-1581.
62. Levitt, D. G. 1978a. Electrostatic calculations for an ion channel. (1) Energy and potential profiles and interactions between ions. Biophys. J. 22:209-219.
63. Levitt, D. G. 1978b. Electrostatic calculations for an ion channel. (2) Kinetic behaviour of the gramicidin A channel. Biophys. J. 22:219-247.
64. Levitt, D. G. 1991. General continuum theory for multi-ion channel. (2) Application to acetylcholine channel. Biophys. J. 59:278-288.
65. Luty, B. A., and W. F. van Gunsteren. 1996. Calculating electrostatic interactions using the particle-particle particle-mesh method with nonperiodic long-range interactions. J. Phys. Chem. 100:2581-2587.
66. Mahanty, J., and B. W. Ninham. 1976. Dispersion Forces. Academic Press, New York.
67. Mohan, V., M. E. Davis, J. A. McCammon, and B. M. Pettitt. 1992. Continuum model calculations of solvation free energies: accurate evaluation of electrostatic contributions. J. Phys. Chem. 96:6428-6431.
68. Oiki, S., V. Madison, and M. Montal. 1990. Bundles of amphipathic transmembrane α-helices as a structural motif for ion-conducting channel proteins: studies on sodium channels and acetylcholine receptors. Proteins. 8:226-236.
69. Parsegian, V. A. 1969. Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature. 221:844-846.
70. Parsegian, V. A. 1975. Ion-membrane interactions and structural forces. Ann. N. Y. Acad. Sci. 264:161-174.
71. Partenskii, M. B., M. Cai, and P. C. Jordan. 1991. A dipolar chain model for the electrostatics of transmembrane ion channels. Chem. Phys. 153: 125-131.
72. Partenskii, M. B., V. Dorman, and P. C. Jordan. 1994. Influence of a channel-forming peptide on energy barriers to ion permeation, viewed from a continuum dielectric perspective. Biophys. J. 67:1429-1438.
73. Partenskii, M. B., and P. C. Jordan. 1992a. Nonlinear dielectric behavior of water in transmembrane ion channels: ion energy barriers and channel dielectric constant. J. Phys. Chem. 96:3906-3910.
74. Partenskii, M. B., and P. C. Jordan. 1992b. Theoretical perspectives on ion-channel electrostatics - continuum and microscopic approaches. Q. Rev. Biophys. 25:477-510.
75. Pearlman, D. A., and S.-H. Kim. 1990. Atomic charges for DNA constituents derived from single-crystal X-ray diffraction data. J. Mol. Biol. 211:171-187.
76. Polymeropoulos, E. E., and J. Brickmann. 1985. Molecular dynamics of ion transport through transmembrane mode channels. In Annual Reviews in Biophysics and Biophysical Chemistry. D. M. Engelman, C. R. Cantor, and P. Thomas D. editors. 315-330.
77. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Fannery. 1992. Numerical Recipes in C. Cambridge University Press, Cambridge.
78. Reynolds, C. A., J. W. Essex, and W. G. Richards. 1992. Atomic charges for variable molecular conformations. J. Am. Chem. Soc. 114: 9075-9079.
79. + in the gramicidin channel. Chem. Phys. Lett. 212:231-240.
80. Roux, B., and M. Karplus. 1994. Molecular dynamics simulations of the gramicidin channel. Annu. Rev. Biophys. Biomol. Struct. 23:731-761.
81. Sancho, M., M. B. Partenskii, V. Dorman, and P. C. Jordan. 1995. Extended dipolar chain model for ion channels - electrostriction effects and the translocational energy barrier. Biophys. J. 68:427-433.
82. Sansom, M. S. P. 1993. Structure and function of channel-forming peptaibols. Q. Rev. Biophys. 26:365-421.
83. Schaefer, M., and M. Karplus. 1996. A comprehensive analytical treatment of continuum electrostatics. J. Phys. Chem. 100:1578-1599.
84. Schiffer, C. A., J. W. Caldwell, P. A. Kollman, and R. M. Stroud. 1993. Protein structure prediction with a combined solvation free energy-molecular mechanics force-field. Mol. Simul. 10:121.
85. Schreiber, H., and O. Steinhauser. 1992. Cutoff size does strongly influence molecular dynamics results on solvated polypeptides. Biochemistry. 31:5856-5860.
86. Sharp, K. 1991. Incorporating solvent and ion screening into molecular dynamics using the finite-difference Poisson - Boltzmann method. J. Comput. Chem. 12:454-468.
87. Sharp, K. A. 1993. Inclusion of solvent effects in molecular mechanics force fields. In Computer Simulations of Biomolecular Systems: Theoretical and Experimental Applications. W. F. van Gunsteren, P. K. Weiner, and A. J. Wilkinson, editors. ESCOM, Leiden. 147-160.
88. Shaw, P. B. 1985. Theory of the Poissons Green's function for discontinuous dielectric media with an application to protein biophysics. Phys. Rev. A. 32:2476-2487.
89. Simonson, T., D. Perahia, and A. T. Brünger. 1991. Microscopic theory of the dielectric properties of proteins. J. Mol. Biol. 218:859-886.
90. Singh, U. C., P. K. Weiner, J. Caldwell, and P. Kollman. 1989. AMBER 3.0 Revision A, Assisted Model Building with Energy Refinement. Department of Pharmaceutical Chemistry, School of Pharmacy, University of California, San Francisco, CA.
91. Sklenar, H., F. Eisenhaber, M. Poncin, and R. Lavery. 1990. Including solvent and counterion effects in the force fields of macromolecular mechanics: the field integrated electrostatic approach (FIESTA). In Theoretical Biochemistry and Molecular Biophysics. D. L. Beveridge, and R. Lavery, editors. Adenine Press, New York. 317-335.
92. Smythe, W. R. 1939. Static and Dynamic Electricity. McGraw-Hill, New York.
93. Soumpasis, D. M., M. Robert-Nicoud, and T. M. Jovin. 1987. B-Z DNA conformational transition in 1:1 electrolytes: dependence upon counterion size. FEBS Lett. 213:341-344.
94. Stakold, I. P. 1968. Boundary Value Problems of Mathematical Physics. Macmillan, New York.
95. Still, W. C., A. Tempczyk, R. C. Hawley. and T. Hendrickson. 1990. Semianalytical treatment of solvation for molecular mechanics and dynamics. J. Am. Chem. Soc. 112:6127-6129.
96. Stokes, R. H. 1964. The van der Waals radii of gaseous ions of the noble gas structure in relation to hydration energies. J. Am. Chem. Soc. 86:979-982.
97. Stouten, P. F. W., C. Froemmel, H. Nakamura, and C. Sander. 1993. An effective solvation term based on atomic occupancies for use in protein simulations. Mol. Simul. 10:97-120.
98. Syganow, A., and E. von Kitzing. 1995. The integral weak diffusion and diffusion approximations applied to ion transport through biological ion channels. J. Phys. Chem. 99:12030-12040.
99. Tlewelling, R. F., and W. L. Hubbel. 1986. The membrane dipole potential in a total membrane potential model. Biophys. J. 49:541-552.
100. Toyoshima, C., and N. Unwin. 1988. Ion channel of acetylcholine receptor reconstructed from images of postsynaptic membranes. Nature. 336: 247-250.
101. Tredgold, R. H., and P. N. Hole. 1976. Dielectric behaviour of dry synthetic polypeptides. Biochim. Biophys. Acta. 443:137-142.
102. Unwin, N. 1993. Nicotinic acetylcholine receptor at 9 Å resolution. J. Mol. Biol. 229:1101-1124.
103. Unwin, N. 1995. Acetylcholine-receptor channel imaged in the open state. Nature. 373:37-43.
104. van Gunsteren, W. F., and H. J. C. Berendsen. 1990. Computer simulation of molecular dynamics: methodology, applications, and perspectives in chemistry. Angew. Chem. Int. Ed. Engl. 29:992-1023.
105. Veresov, V. G. 1994. A Brownian dynamics study of direct ion passage through potassium channel. Biologicheskie Membrany. 11:209-216.
106. Villarroel, A., and B. Sakmann. 1992. Threonine in the selectivity filter of the acetylcholine receptor channel. Biophys. J. 62:196-208.
107. von Kitzing, E. 1995. Structure modeling of the acetylcholine receptor channel and related ligand gated channels. In Modelling of Biomolecular Structures and Mechanisms. A. Pullman. J. Jortner, and B. Pullman, editors. Kluwer Academic Publishers, Dortrecht. 39-57.
108. Vorobjev, Y. N., J. A. Grant, and H. A. Scheraga. 1992. A combined iterative and boundary element approach for solution of the nonlinear Poisson-Boltzmann equation. J. Am. Chem. Soc. 114:3189-3196.
109. Warshel, A. 1987. What about protein polarity? Nature. 330:15-16.
110. Weiner, S. J., P. A. Kollman, D. A. Case, U. C. Singh, C. Ghio, G. Alagona, S. J. Profeta. and P. Weiner. 1984. A new force field for molecular mechanical simulation of nucleic acids and proteins. J. Am. Chem. Soc. 106:765-784.
111. Zacharias, M., B. A. Luty, M. E. Davis, and J. A. McCammon. 1994. Combined conformational search and finite-difference Poisson-Boltzmann approach for flexible docking - application to an operator mutation in the lambda-repressor-operator complex. J. Mol. Biol. 238: 455-465.
112. Zauhar, R. J., and R. S. Morgan. 1985. A new method for computing the macromolecular electric potential. J. Mol. Biol. 186:815-820.
113. Zauhar, R. J., and R. S. Morgan. 1988. The rigorous computation of the molecular electric potential. J. Comput. Chem. 9:171-187.
114. Zhexin, X., H. Fuhua, and S. Yunyu. 1994. Calculation of solvation energy with a combination of the boundary element method and PDLD model. J. Phys. Chem. 98:12782-12788.